UNIVERSAL speed of light in vacuum c, c 0 299 792 458 m s 1 exact magnetic constant µ 0 4π 10 7 N A 2 = 12.566 370 614... 10 7 N A 2 exact electric constant 1/µ 0 c 2 ɛ 0 8.854 187 817... 10 12 F m 1 exact characteristic impedance of vacuum µ 0 c Z 0 376.730 313 461... Ω exact Newtonian constant of gravitation G 6.674 08(31) 10 11 m 3 kg 1 s 2 4.7 10 5 G/ hc 6.708 61(31) 10 39 (GeV/c 2 ) 2 4.7 10 5 Planck constant h 6.626 070 040(81) 10 34 J s 1.2 10 8 4.135 667 662(25) 10 15 ev s 6.1 10 9 h/2π h 1.054 571 800(13) 10 34 J s 1.2 10 8 6.582 119 514(40) 10 16 ev s 6.1 10 9 hc 197.326 9788(12) MeV fm 6.1 10 9 Planck mass ( hc/g) 1/2 m P 2.176 470(51) 10 8 kg 2.3 10 5 energy equivalent m P c 2 1.220 910(29) 10 19 GeV 2.3 10 5 Planck temperature ( hc 5 /G) 1/2 /k T P 1.416 808(33) 10 32 K 2.3 10 5 Planck length h/m P c = ( hg/c 3 ) 1/2 l P 1.616 229(38) 10 35 m 2.3 10 5 Planck time l P /c = ( hg/c 5 ) 1/2 t P 5.391 16(13) 10 44 s 2.3 10 5 ELECTROMAGNETIC elementary charge e 1.602 176 6208(98) 10 19 C 6.1 10 9 e/h 2.417 989 262(15) 10 14 A J 1 6.1 10 9 magnetic flux quantum h/2e Φ 0 2.067 833 831(13) 10 15 Wb 6.1 10 9 conductance quantum 2e 2 /h G 0 7.748 091 7310(18) 10 5 S 2.3 10 10 inverse of conductance quantum G 1 0 12 906.403 7278(29) Ω 2.3 10 10 Josephson constant 1 2e/h K J 483 597.8525(30) 10 9 Hz V 1 6.1 10 9 von Klitzing constant 2 h/e 2 = µ 0 c/2α R K 25 812.807 4555(59) Ω 2.3 10 10 Bohr magneton e h/2m e µ B 927.400 9994(57) 10 26 J T 1 6.2 10 9 5.788 381 8012(26) 10 5 ev T 1 4.5 10 10 µ B /h 13.996 245 042(86) 10 9 Hz T 1 6.2 10 9 µ B /hc 46.686 448 14(29) m 1 T 1 6.2 10 9 µ B /k 0.671 714 05(39) K T 1 5.7 10 7 nuclear magneton e h/2m p µ N 5.050 783 699(31) 10 27 J T 1 6.2 10 9 3.152 451 2550(15) 10 8 ev T 1 4.6 10 10 µ N /h 7.622 593 285(47) MHz T 1 6.2 10 9 µ N /hc 2.542 623 432(16) 10 2 m 1 T 1 6.2 10 9 µ N /k 3.658 2690(21) 10 4 K T 1 5.7 10 7 ATOMIC AND NUCLEAR General fine-structure constant e 2 /4πɛ 0 hc α 7.297 352 5664(17) 10 3 2.3 10 10 inverse fine-structure constant α 1 137.035 999 139(31) 2.3 10 10 Rydberg constant α 2 m e c/2h R 10 973 731.568 508(65) m 1 5.9 10 12 R c 3.289 841 960 355(19) 10 15 Hz 5.9 10 12 R hc 2.179 872 325(27) 10 18 J 1.2 10 8 13.605 693 009(84) ev 6.1 10 9 Bohr radius α/4πr = 4πɛ 0 h 2 /m e e 2 a 0 0.529 177 210 67(12) 10 10 m 2.3 10 10 Hartree energy e 2 /4πɛ 0 a 0 = 2R hc = α 2 m e c 2 E h 4.359 744 650(54) 10 18 J 1.2 10 8 27.211 386 02(17) ev 6.1 10 9 quantum of circulation h/2m e 3.636 947 5486(17) 10 4 m 2 s 1 4.5 10 10 Page 1
h/m e 7.273 895 0972(33) 10 4 m 2 s 1 4.5 10 10 Electroweak Fermi coupling constant 3 G F /( hc) 3 1.166 3787(6) 10 5 GeV 2 5.1 10 7 weak mixing angle 4 θ W (on-shell scheme) sin 2 θ W = s 2 W 1 (m W/m Z ) 2 sin 2 θ W 0.2223(21) 9.5 10 3 Electron, e electron mass m e 9.109 383 56(11) 10 31 kg 1.2 10 8 5.485 799 090 70(16) 10 4 u 2.9 10 11 energy equivalent m e c 2 8.187 105 65(10) 10 14 J 1.2 10 8 0.510 998 9461(31) MeV 6.2 10 9 electron-muon mass ratio m e /m µ 4.836 331 70(11) 10 3 2.2 10 8 electron-tau mass ratio m e /m τ 2.875 92(26) 10 4 9.0 10 5 electron-proton mass ratio m e /m p 5.446 170 213 52(52) 10 4 9.5 10 11 electron-neutron mass ratio m e /m n 5.438 673 4428(27) 10 4 4.9 10 10 electron-deuteron mass ratio m e /m d 2.724 437 107 484(96) 10 4 3.5 10 11 electron-triton mass ratio m e /m t 1.819 200 062 203(84) 10 4 4.6 10 11 electron-helion mass ratio m e /m h 1.819 543 074 854(88) 10 4 4.9 10 11 electron to alpha particle mass ratio m e /m α 1.370 933 554 798(45) 10 4 3.3 10 11 electron charge to mass quotient e/m e 1.758 820 024(11) 10 11 C kg 1 6.2 10 9 electron molar mass N A m e M(e), M e 5.485 799 090 70(16) 10 7 kg mol 1 2.9 10 11 Compton wavelength h/m e c λ C 2.426 310 2367(11) 10 12 m 4.5 10 10 λ C /2π = αa 0 = α 2 /4πR λ C 386.159 267 64(18) 10 15 m 4.5 10 10 classical electron radius α 2 a 0 r e 2.817 940 3227(19) 10 15 m 6.8 10 10 Thomson cross section (8π/3)re 2 σ e 0.665 245 871 58(91) 10 28 m 2 1.4 10 9 electron magnetic moment µ e 928.476 4620(57) 10 26 J T 1 6.2 10 9 to Bohr magneton ratio µ e /µ B 1.001 159 652 180 91(26) 2.6 10 13 to nuclear magneton ratio µ e /µ N 1838.281 972 34(17) 9.5 10 11 electron magnetic moment anomaly µ e /µ B 1 a e 1.159 652 180 91(26) 10 3 2.3 10 10 electron g-factor 2(1 + a e ) g e 2.002 319 304 361 82(52) 2.6 10 13 electron-muon magnetic moment ratio µ e /µ µ 206.766 9880(46) 2.2 10 8 electron-proton magnetic moment ratio µ e /µ p 658.210 6866(20) 3.0 10 9 electron to shielded proton magnetic moment ratio (H 2 O, sphere, 25 C) µ e /µ p 658.227 5971(72) 1.1 10 8 electron-neutron magnetic moment ratio µ e /µ n 960.920 50(23) 2.4 10 7 electron-deuteron magnetic moment ratio µ e /µ d 2143.923 499(12) 5.5 10 9 electron to shielded helion magnetic moment ratio (gas, sphere, 25 C) µ e /µ h 864.058 257(10) 1.2 10 8 electron gyromagnetic ratio 2 µ e / h γ e 1.760 859 644(11) 10 11 s 1 T 1 6.2 10 9 γ e /2π 28 024.951 64(17) MHz T 1 6.2 10 9 Muon, µ muon mass m µ 1.883 531 594(48) 10 28 kg 2.5 10 8 0.113 428 9257(25) u 2.2 10 8 energy equivalent m µ c 2 1.692 833 774(43) 10 11 J 2.5 10 8 105.658 3745(24) MeV 2.3 10 8 muon-electron mass ratio m µ /m e 206.768 2826(46) 2.2 10 8 muon-tau mass ratio m µ /m τ 5.946 49(54) 10 2 9.0 10 5 muon-proton mass ratio m µ /m p 0.112 609 5262(25) 2.2 10 8 Page 2
muon-neutron mass ratio m µ /m n 0.112 454 5167(25) 2.2 10 8 muon molar mass N A m µ M(µ), M µ 0.113 428 9257(25) 10 3 kg mol 1 2.2 10 8 muon Compton wavelength h/m µ c λ C,µ 11.734 441 11(26) 10 15 m 2.2 10 8 λ C,µ /2π λ C,µ 1.867 594 308(42) 10 15 m 2.2 10 8 muon magnetic moment µ µ 4.490 448 26(10) 10 26 J T 1 2.3 10 8 to Bohr magneton ratio µ µ /µ B 4.841 970 48(11) 10 3 2.2 10 8 to nuclear magneton ratio µ µ /µ N 8.890 597 05(20) 2.2 10 8 muon magnetic moment anomaly µ µ /(e h/2m µ ) 1 a µ 1.165 920 89(63) 10 3 5.4 10 7 muon g-factor 2(1 + a µ ) g µ 2.002 331 8418(13) 6.3 10 10 muon-proton magnetic moment ratio µ µ /µ p 3.183 345 142(71) 2.2 10 8 Tau, τ tau mass 5 m τ 3.167 47(29) 10 27 kg 9.0 10 5 1.907 49(17) u 9.0 10 5 energy equivalent m τ c 2 2.846 78(26) 10 10 J 9.0 10 5 1776.82(16) MeV 9.0 10 5 tau-electron mass ratio m τ /m e 3477.15(31) 9.0 10 5 tau-muon mass ratio m τ /m µ 16.8167(15) 9.0 10 5 tau-proton mass ratio m τ /m p 1.893 72(17) 9.0 10 5 tau-neutron mass ratio m τ /m n 1.891 11(17) 9.0 10 5 tau molar mass N A m τ M(τ), M τ 1.907 49(17) 10 3 kg mol 1 9.0 10 5 tau Compton wavelength h/m τ c λ C,τ 0.697 787(63) 10 15 m 9.0 10 5 λ C,τ /2π λ C,τ 0.111 056(10) 10 15 m 9.0 10 5 Proton, p proton mass m p 1.672 621 898(21) 10 27 kg 1.2 10 8 1.007 276 466 879(91) u 9.0 10 11 energy equivalent m p c 2 1.503 277 593(18) 10 10 J 1.2 10 8 938.272 0813(58) MeV 6.2 10 9 proton-electron mass ratio m p /m e 1836.152 673 89(17) 9.5 10 11 proton-muon mass ratio m p /m µ 8.880 243 38(20) 2.2 10 8 proton-tau mass ratio m p /m τ 0.528 063(48) 9.0 10 5 proton-neutron mass ratio m p /m n 0.998 623 478 44(51) 5.1 10 10 proton charge to mass quotient e/m p 9.578 833 226(59) 10 7 C kg 1 6.2 10 9 proton molar mass N A m p M(p), M p 1.007 276 466 879(91) 10 3 kg mol 1 9.0 10 11 proton Compton wavelength h/m p c λ C,p 1.321 409 853 96(61) 10 15 m 4.6 10 10 λ C,p /2π λ C,p 0.210 308 910 109(97) 10 15 m 4.6 10 10 proton rms charge radius r p 0.8751(61) 10 15 m 7.0 10 3 proton magnetic moment µ p 1.410 606 7873(97) 10 26 J T 1 6.9 10 9 to Bohr magneton ratio µ p /µ B 1.521 032 2053(46) 10 3 3.0 10 9 to nuclear magneton ratio µ p /µ N 2.792 847 3508(85) 3.0 10 9 proton g-factor 2µ p /µ N g p 5.585 694 702(17) 3.0 10 9 proton-neutron magnetic moment ratio µ p /µ n 1.459 898 05(34) 2.4 10 7 shielded proton magnetic moment µ p 1.410 570 547(18) 10 26 J T 1 1.3 10 8 (H 2 O, sphere, 25 C) to Bohr magneton ratio µ p/µ B 1.520 993 128(17) 10 3 1.1 10 8 to nuclear magneton ratio µ p/µ N 2.792 775 600(30) 1.1 10 8 proton magnetic shielding correction 1 µ p/µ p (H 2 O, sphere, 25 C) σ p 25.691(11) 10 6 4.4 10 4 Page 3
proton gyromagnetic ratio 2µ p / h γ p 2.675 221 900(18) 10 8 s 1 T 1 6.9 10 9 γ p /2π 42.577 478 92(29) MHz T 1 6.9 10 9 shielded proton gyromagnetic ratio 2µ p/ h (H 2 O, sphere, 25 C) γ p 2.675 153 171(33) 10 8 s 1 T 1 1.3 10 8 γ p/2π 42.576 385 07(53) MHz T 1 1.3 10 8 Neutron, n neutron mass m n 1.674 927 471(21) 10 27 kg 1.2 10 8 1.008 664 915 88(49) u 4.9 10 10 energy equivalent m n c 2 1.505 349 739(19) 10 10 J 1.2 10 8 939.565 4133(58) MeV 6.2 10 9 neutron-electron mass ratio m n /m e 1838.683 661 58(90) 4.9 10 10 neutron-muon mass ratio m n /m µ 8.892 484 08(20) 2.2 10 8 neutron-tau mass ratio m n /m τ 0.528 790(48) 9.0 10 5 neutron-proton mass ratio m n /m p 1.001 378 418 98(51) 5.1 10 10 neutron-proton mass difference m n m p 2.305 573 77(85) 10 30 kg 3.7 10 7 0.001 388 449 00(51) u 3.7 10 7 energy equivalent (m n m p )c 2 2.072 146 37(76) 10 13 J 3.7 10 7 1.293 332 05(48) MeV 3.7 10 7 neutron molar mass N A m n M(n), M n 1.008 664 915 88(49) 10 3 kg mol 1 4.9 10 10 neutron Compton wavelength h/m n c λ C,n 1.319 590 904 81(88) 10 15 m 6.7 10 10 λ C,n /2π λ C,n 0.210 019 415 36(14) 10 15 m 6.7 10 10 neutron magnetic moment µ n 0.966 236 50(23) 10 26 J T 1 2.4 10 7 to Bohr magneton ratio µ n /µ B 1.041 875 63(25) 10 3 2.4 10 7 to nuclear magneton ratio µ n /µ N 1.913 042 73(45) 2.4 10 7 neutron g-factor 2µ n /µ N g n 3.826 085 45(90) 2.4 10 7 neutron-electron magnetic moment ratio µ n /µ e 1.040 668 82(25) 10 3 2.4 10 7 neutron-proton magnetic moment ratio µ n /µ p 0.684 979 34(16) 2.4 10 7 neutron to shielded proton magnetic moment ratio (H 2 O, sphere, 25 C) µ n /µ p 0.684 996 94(16) 2.4 10 7 neutron gyromagnetic ratio 2 µ n / h γ n 1.832 471 72(43) 10 8 s 1 T 1 2.4 10 7 γ n /2π 29.164 6933(69) MHz T 1 2.4 10 7 Deuteron, d deuteron mass m d 3.343 583 719(41) 10 27 kg 1.2 10 8 2.013 553 212 745(40) u 2.0 10 11 energy equivalent m d c 2 3.005 063 183(37) 10 10 J 1.2 10 8 1875.612 928(12) MeV 6.2 10 9 deuteron-electron mass ratio m d /m e 3670.482 967 85(13) 3.5 10 11 deuteron-proton mass ratio m d /m p 1.999 007 500 87(19) 9.3 10 11 deuteron molar mass N A m d M(d), M d 2.013 553 212 745(40) 10 3 kg mol 1 2.0 10 11 deuteron rms charge radius r d 2.1413(25) 10 15 m 1.2 10 3 deuteron magnetic moment µ d 0.433 073 5040(36) 10 26 J T 1 8.3 10 9 to Bohr magneton ratio µ d /µ B 0.466 975 4554(26) 10 3 5.5 10 9 to nuclear magneton ratio µ d /µ N 0.857 438 2311(48) 5.5 10 9 deuteron g-factor µ d /µ N g d 0.857 438 2311(48) 5.5 10 9 deuteron-electron magnetic moment ratio µ d /µ e 4.664 345 535(26) 10 4 5.5 10 9 deuteron-proton magnetic moment ratio µ d /µ p 0.307 012 2077(15) 5.0 10 9 deuteron-neutron magnetic moment ratio µ d /µ n 0.448 206 52(11) 2.4 10 7 Triton, t Page 4
triton mass m t 5.007 356 665(62) 10 27 kg 1.2 10 8 3.015 500 716 32(11) u 3.6 10 11 energy equivalent m t c 2 4.500 387 735(55) 10 10 J 1.2 10 8 2808.921 112(17) MeV 6.2 10 9 triton-electron mass ratio m t /m e 5496.921 535 88(26) 4.6 10 11 triton-proton mass ratio m t /m p 2.993 717 033 48(22) 7.5 10 11 triton molar mass N A m t M(t), M t 3.015 500 716 32(11) 10 3 kg mol 1 3.6 10 11 triton magnetic moment µ t 1.504 609 503(12) 10 26 J T 1 7.8 10 9 to Bohr magneton ratio µ t /µ B 1.622 393 6616(76) 10 3 4.7 10 9 to nuclear magneton ratio µ t /µ N 2.978 962 460(14) 4.7 10 9 triton g-factor 2µ t /µ N g t 5.957 924 920(28) 4.7 10 9 Helion, h helion mass m h 5.006 412 700(62) 10 27 kg 1.2 10 8 3.014 932 246 73(12) u 3.9 10 11 energy equivalent m h c 2 4.499 539 341(55) 10 10 J 1.2 10 8 2808.391 586(17) MeV 6.2 10 9 helion-electron mass ratio m h /m e 5495.885 279 22(27) 4.9 10 11 helion-proton mass ratio m h /m p 2.993 152 670 46(29) 9.6 10 11 helion molar mass N A m h M(h), M h 3.014 932 246 73(12) 10 3 kg mol 1 3.9 10 11 helion magnetic moment µ h 1.074 617 522(14) 10 26 J T 1 1.3 10 8 to Bohr magneton ratio µ h /µ B 1.158 740 958(14) 10 3 1.2 10 8 to nuclear magneton ratio µ h /µ N 2.127 625 308(25) 1.2 10 8 helion g-factor 2µ h /µ N g h 4.255 250 616(50) 1.2 10 8 shielded helion magnetic moment µ h 1.074 553 080(14) 10 26 J T 1 1.3 10 8 (gas, sphere, 25 C) to Bohr magneton ratio µ h /µ B 1.158 671 471(14) 10 3 1.2 10 8 to nuclear magneton ratio µ h /µ N 2.127 497 720(25) 1.2 10 8 shielded helion to proton magnetic moment ratio (gas, sphere, 25 C) µ h /µ p 0.761 766 5603(92) 1.2 10 8 shielded helion to shielded proton magnetic moment ratio (gas/h 2 O, spheres, 25 C) µ h /µ p 0.761 786 1313(33) 4.3 10 9 shielded helion gyromagnetic ratio 2 µ h / h (gas, sphere, 25 C) γ h 2.037 894 585(27) 10 8 s 1 T 1 1.3 10 8 γ h /2π 32.434 099 66(43) MHz T 1 1.3 10 8 Alpha particle, α alpha particle mass m α 6.644 657 230(82) 10 27 kg 1.2 10 8 4.001 506 179 127(63) u 1.6 10 11 energy equivalent m α c 2 5.971 920 097(73) 10 10 J 1.2 10 8 3727.379 378(23) MeV 6.2 10 9 alpha particle to electron mass ratio m α /m e 7294.299 541 36(24) 3.3 10 11 alpha particle to proton mass ratio m α /m p 3.972 599 689 07(36) 9.2 10 11 alpha particle molar mass N A m α M(α), M α 4.001 506 179 127(63) 10 3 kg mol 1 1.6 10 11 PHYSICOCHEMICAL Avogadro constant N A, L 6.022 140 857(74) 10 23 mol 1 1.2 10 8 atomic mass constant m u = 1 12 m(12 C) = 1 u m u 1.660 539 040(20) 10 27 kg 1.2 10 8 energy equivalent m u c 2 1.492 418 062(18) 10 10 J 1.2 10 8 931.494 0954(57) MeV 6.2 10 9 Page 5
Faraday constant 6 N A e F 96 485.332 89(59) C mol 1 6.2 10 9 molar Planck constant N A h 3.990 312 7110(18) 10 10 J s mol 1 4.5 10 10 N A hc 0.119 626 565 582(54) J m mol 1 4.5 10 10 molar gas constant R 8.314 4598(48) J mol 1 K 1 5.7 10 7 Boltzmann constant R/N A k 1.380 648 52(79) 10 23 J K 1 5.7 10 7 8.617 3303(50) 10 5 ev K 1 5.7 10 7 k/h 2.083 6612(12) 10 10 Hz K 1 5.7 10 7 k/hc 69.503 457(40) m 1 K 1 5.7 10 7 molar volume of ideal gas RT/p T = 273.15 K, p = 100 kpa V m 22.710 947(13) 10 3 m 3 mol 1 5.7 10 7 Loschmidt constant N A /V m n 0 2.651 6467(15) 10 25 m 3 5.7 10 7 molar volume of ideal gas RT/p T = 273.15 K, p = 101.325 kpa V m 22.413 962(13) 10 3 m 3 mol 1 5.7 10 7 Loschmidt constant N A /V m n 0 2.686 7811(15) 10 25 m 3 5.7 10 7 Sackur-Tetrode (absolute entropy) constant 7 5 2 + ln[(2πm ukt 1 /h 2 ) 3/2 kt 1 /p 0 ] T 1 = 1 K, p 0 = 100 kpa S 0 /R 1.151 7084(14) 1.2 10 6 T 1 = 1 K, p 0 = 101.325 kpa 1.164 8714(14) 1.2 10 6 Stefan-Boltzmann constant (π 2 /60)k 4 / h 3 c 2 σ 5.670 367(13) 10 8 W m 2 K 4 2.3 10 6 first radiation constant 2πhc 2 c 1 3.741 771 790(46) 10 16 W m 2 1.2 10 8 first radiation constant for spectral radiance 2hc 2 c 1L 1.191 042 953(15) 10 16 W m 2 sr 1 1.2 10 8 second radiation constant hc/k c 2 1.438 777 36(83) 10 2 m K 5.7 10 7 Wien displacement law constants b = λ max T = c 2 /4.965 114 231... b 2.897 7729(17) 10 3 m K 5.7 10 7 b = ν max /T = 2.821 439 372... c/c 2 b 5.878 9238(34) 10 10 Hz K 1 5.7 10 7 1 See the Adopted values table for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect. 2 See the Adopted values table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect. 3 Value recommended by the Particle Data Group (Olive et al., 2014). 4 Based on the ratio of the masses of the W and Z bosons m W/m Z recommended by the Particle Data Group (Olive et al., 2014). The value for sin 2 θ W they recommend, which is based on a particular variant of the modified minimal subtraction (MS) scheme, is sin 2 ˆθW(M Z) = 0.231 26(5). 5 This and all other values involving m τ are based on the value of m τc 2 in MeV recommended by the Particle Data Group (Olive et al., 2014). 6 The numerical value of F to be used in coulometric chemical measurements is 96 485.3251(12) [1.2 10 8 ] when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants K J 90 and R K 90 given in the Adopted values table. 7 The entropy of an ideal monoatomic gas of relative atomic mass A r is given by S = S 0 + 3 R ln 2 Ar R ln(p/p0) + 5 R ln(t/k). 2 Page 6